Yr 7 Simple Linear Equations, integer answers only

The student will be given 2 integers between -9 and +9 to add together.

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This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Putting algebraic fractions into their simplest forms

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Choosing whether given random variables are qualitative or quantitative.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

A collection of questions (frequently updated) to demonstrate the usage of the Logic extension.

Current questions:

• Make syllogisms (either valid, invalid or valid under an additional assumption);
• Write statements in Polish and reverse Polish notation, find the truth table, determine satisfiability;
• Test whether a collection of statements $\Gamma$ models a statement $\phi$;
• Write the Disjunctive and Conjunctive Normal Forms for a statement.

Needs the Logic Extension!

Yr 7 Simple Linear Equations, integer answers only

Yr 7 Simple Linear Equations, integer answers only

Questions on presenting data in charts or tables.

Questions on the subtleties and pitfalls of methods of data collection.

Calculate and work with measures of central tendency such as mean, median and mode, and measures of spread such as range and standard deviation.

Questions on the subtleties and pitfalls of methods of data collection.

Questions on presenting data in charts or tables.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

A multiple linear regression model of the form:

\[Y=\beta_0+\beta_1X_1+ \beta_2X_2+\beta_3X_3+\beta_4X_4+\epsilon \]

is fitted to some data in Minitab which generates a table showing estimates of the parameters with associated $p$-values. Determine which variable to exclude first.

Given two distributions, calculate the measures of average and spread and make some decisions based on the results.

A multiple linear regression model of the form:

\[Y=\beta_0+\beta_1X_1+ \beta_2X_2+\beta_3X_3+\beta_4X_4+\epsilon \]

is fitted to some data in Minitab which generates a table showing estimates of the parameters with associated $p$-values. Determine which variable to exclude first.

Questions on Kruskal-Wallis and Friedman tests.

Statistics and probability. A question on two factor ANOVA.

Three questions on parametric hypothesis testing and confidence intervals, aimed at psychology students.

Find the sum of two 2-dimensional vectors, graphically and exactly using the parallelogram rule.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

Calculate relative frequencies in a variety of scenarios.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Two questions testing the application of the Sine Rule when given two sides and an angle. In this question, the triangle is always acute and one of the given side lengths is opposite the given angle.

Questions about the properties of different types of triangles.